An investigation into procedural (in)variance in the valuation of mortality risk reductions

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Abstract

This study investigates whether elicited preferences are affected by the presentation of mortality risks in a stated preference survey. We elicited willingness to pay for public risk reducing initiatives under three different but outcome equivalent presentation format. Results from a discrete choice experiment demonstrate that presentation format influences the valuation of mortality risk reductions, which to varying degrees depends on the respondent's level of concern and numeracy. Marginal willingness to pay for a risk reduction increases significantly when framed in terms of avoided fatalities compared to corresponding frequencies. Furthermore, we find that less numerate respondents are more influenced by the inclusion of the number of fatalities in the presentation format. The same pattern is observed for respondents who express a higher degree of concern for a traffic accident.

Introduction

Valuation of mortality risk reductions constitutes an important input to cost-benefit analysis of many environmental policies such as air pollution reducing initiatives. The welfare economic approach to valuing reductions in mortality risk requires an estimate of the individual's rate of substitution between wealth and risk (Jones-Lee et al., 1985). Several methods can be used to estimate this trade off including stated preference (SP) methods such as contingent valuation and choice experiments. The estimated absolute value of a marginal risk reduction, defined as the Value of Statistical life (VSL) is obtained by dividing the estimated willingness to pay (WTP) by the corresponding risk reduction. While some SP studies have investigated (in)sensitivity to the magnitude of risk reduction (see e.g. Andersson et al., 2016), studies on the effect of different but outcome equivalent presentation formats are scarce. Gyrd-Hansen et al. (2003) and others have found individuals to be sensitive to whether risk information is presented as absolute or relative risk reductions, and Zhai and Suzuki (2008) have found that the larger the denominator of the fraction (e.g. 1/100 versus 10/1000), the less the WTP for a given risk reduction.

The benefit of public risk reducing initiatives can either be presented as a change in the risk of dying (expressed as frequencies or probabilities), or as the equivalent expected total number of fatalities avoided/lives saved over a given population.1 The latter has also been termed the ‘community analogy’ (Calman and Royston, 1997). To illustrate, a reduction in risk from 2 in 10,000 to 1 in 10,000 in a community with 500,000 individuals can be presented as either a standard frequency (1 in 10,000) or a relative risk reduction (50%), or presented as a ‘community analogy’ frequency based on the number of individuals in the community (50 fatalities avoided). According to the assumption of procedural invariance (Tversky and Thaler, 1990), presentation format should not matter as long as the expected outcome is the same. The risk reduction format (frequency and/or relative risk reduction) has been used in previous SP studies, see eg. Jones-Lee et al. (1985) and Alberini and Scasny (2011), whereas the community analogy has been used for estimating WTP in eg. Andersson et al. (2016) and Rheinberger (2011). No study has so far attempted to systematically compare the effect of these different presentation formats on the implied valuations of outcomes, and the choice of presentation format appears to be rather idiosyncratic.

There is a large literature showing that risks and risk changes are not always perceived correctly by individuals, and that individuals have difficulties understanding how probabilities influence risk assessments. It has been proposed that affect (i.e. risk as feelings) may serve as a cue for many important judgments involving risk, and that different representations of risks are associated with affect to varying degrees (Finucane et al., 2000). Studies by Slovic and colleagues have showed that presentation of risks in the form of frequencies (e.g. 1 out of 100) created more frightening images than probabilities (Slovic et al., 2002). In addition, Rottenstreich and Hsee (2001) found a more pronounced overweighting of small probabilities relating to affect-rich outcomes compared to affect-poor outcomes. According to Slovic et al. (2002) affective responses occur rapidly and automatically and reliance on such feelings can be characterized as an ‘affect heuristic’.

Furthermore, research in psychology has demonstrated that numeracy skills have important consequences for judgement and decision making, and that inadequate numeracy may be an important barrier to an individual's understanding of risks. There is evidence that numerate individuals are likely to pay more attention to numbers associated with a risk as they comprehend them better and use them in decisions. On the other hand, the less numerate are likely to be informed more by other sources of information such as emotions, implying that they are more susceptible to how messages are framed and how numbers are formatted (Peters et al., 2006; Reyna et al., 2009).

We extend the current literature on valuation of mortality risk reductions by systematically investigating the potential influence that different presentation formats have on the elicited values. For this purpose, a three-way split sample discrete choice experiment (DCE) was conducted that include two types of risk information presented either separately or jointly. Respondents were asked to express their WTP for risk reducing initiatives keeping the size of the outcomes constant across splits (all in the context of traffic). To further our understanding of the underlying causes of variation across formats, we investigate whether numerical abilities and affective feelings can explain some of the observed discrepancies in marginal WTP. As a proxy for the former we use subjective numerical skills whereas for the latter, we use survey responses relating to level of concern for traffic accidents.

We find that presentation format significantly affects preferences and that marginal willingness to pay for a risk reduction increases significantly when framed in terms of avoided fatalities compared to corresponding frequencies. Furthermore, we find evidence that the sensitivity to format is impacted by the numerical ability of the respondents as well as their affective reaction.

Section snippets

Data

The sample was obtained from the Nielsen Company's online panel database in May 2013. The survey sample was representative of the adult Danish population with respect to gender and age. 3600 individuals were invited (by email) to participate in the survey. The response rate in the survey was 17% resulting in a sample of 600 equally split across three treatment groups. For those who started the survey, the completion rate was 77%. Prior to the actual data collection, the survey was tested in an

Results

Descriptive statistics can be found in the online Appendix. No significant differences were found with respect to gender, age, household income, number of individuals in household, and proportion with higher education across the three treatment groups (with the exception of age between FATAL and BOTH). Estimated marginal WTP and 95% CIs are reported in Table 2 whereas Table 3 presents the test statistics for our primary and secondary hypotheses. Finally, regression results are reported in Table

Conclusions

The present study contributes to the broad literature on valuation of mortality risk reductions highlighting another source of the observed disparity in VSL estimates found across SP studies (Lindhjem et al., 2011). We find that the framing of mortality risk plays an important role in the valuation of mortality risk reductions. More specifically, our results demonstrate that describing the effect only in terms of ‘avoided fatalities’ could be argued to cause an overestimation of respondents'

Acknowledgement

This work was carried out as part of the project IMPROSA (Improving Road Safety) supported by the Danish Research Council. The opinions expressed in the article are solely the responsibility of the authors and do not necessarily reflect the views of the research project's sponsors. The authors have no conflicts of interests to declare. We thank Editor Roger von Haefen, Professor Dorte Gyrd-Hansen and two anonymous reviewers for their helpful comments and suggestions.

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    In cases where this assumption does not hold CV responses may be malleable and subject to bias. In particular commentators have long argued that in cases of cognitive overload, respondents may seek to infer information regarding appropriate responses from objectively irrelevant elements of the framing of a valuation question (Tversky and Kahneman, 1973, 1974; Slovic, 1995; Nielsen et al., 2012; Kjær et al., 2018). Indeed, the SP literature reports a number of persistent anomalies; results which suggest that respondents are unable to relate certain valuation questions to a set of standard economic preferences (Chilton et al., 2004; Desvousges et al., 1992; Dolan et al., 2008; Hausman, 2012; Jones-Lee et al., 1995; Jones-Lee and Loomes, 2004; McFadden and Train, 2017).

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